Latent Clustered Causal Models

Abstract

We consider the problem of learning directed graphical models in the presence of latent variables. We define latent clustered causal models as a particular restriction on directed graphical models with latent variables and corresponding clusters of observed nodes, characterized by edges between only observed and latent variables. We discuss this model’s particular applicability towards genomics applications and examine its relationship to prior causal structure recovery work. We show identifiability results on this model and design a consistent three-stage algorithm that discovers clusters of observed nodes, a partial ordering over clusters, and finally, the entire structure over both observed and latent nodes. We also evaluate our method on synthetic datasets and demonstrate its performance in low sample-size regimes.